Kérchy László honlapja

Publikációs lista

On the functional calculus of contractions with nonvanishing unitary asymptotes.

Szerző:

K\'erchy, L.

Forrás:

Mich. Math. J. 37, No.3, 323-338 (1990).

Nyelv:

English

Absztrakt:

Let $T$ be a contraction on a Hilbert space $H$. There exist
a Hilbert space $H'$, a unitary operator $T'$ on $H'$, and an
operator $X: H\to H'$ and such that $T'X=XT$ and such that the
triplet $(H',T',X)$ is `universal' with these properties. The
author calls $T'$ the unitary asymptote of $T$. If $T$ is an
absolute continuous contraction then $T'$ has absolutely continuous
spectral measure, and hence there is a Borel set $\Gamma$ such
that arclength on $\Gamma$ is a saclar measure for $T'$.\par
The
main purpose of this article is to produce a new factorization
technique in the theory of dual algebras. The author illustrates
this technique by providing, along with some new results, a new
proof of the following result of {\it B. Chevreau}, {\it G. Exner}
and {\it C. Pearcy} [Mich. Math. J. 36, 29-62 (1989; Zbl 0677.47001)]:
given $\varepsilon>0$ and $f\in L\sp 1(\Gamma)$, there exist
vectors $x,y\in H$ such that $\Vert x\Vert\Vert y\Vert\leq(1+\varepsilon)\Vert
f\Vert\sb 1$ and $(p(T)x,y)=\int\sb \Gamma pf$ for every polynomial
$p$ in one variable.}
\RV{H.Bercovici (Bloomington)